The absorption mechanism of the second pulse is experimentally and theoretically investigated for high-efficiency microwelding of photosensitive glass by double-pulse irradiation using a femtosecond laser. The transient absorption change during the second pulse irradiation for various energies induced by the first pulse is measured at different delay times. The resulting effects depend on whether the delay time is 0–30 ps (time domain I) or 30– several ns (domain II). By solving rate equations for the proposed electronic processes, the excitation and relaxation times of free electrons in time domain I are estimated to be 0.98 and 20.4 ps, respectively, whereas the relaxation times from the conduction band to a localized state and from the localized state to the valence band in domain II are 104.2 and 714.3 ps, respectively. Single-photon absorption of the second pulse by free electrons dominates in domain I, resulting in high bonding strength. In time domain II, about 46% of the second pulse is absorbed by a single photon due to the localized state, which is responsible for higher bonding strength compared with that prepared by single-pulse irradiation.
© 2013 OSA
Glass microwelding induced by an ultrafast laser has been drawing attention for applications such as optics, microelectromechanical systems, precision machinery, healthcare, and small satellites. Many groups have successfully demonstrated microwelding of various glass including borosilicate [1–9], fused silica [10–14], photosensitive glass [15–17], and others [18–21]. In order to enhance the efficiency of glass microwelding, a new strategy  has been proposed using double-pulse irradiation by an ultrafast laser beam. This technique increases the bonding strength of photosensitive glass welding by 22% relative to that for conventional single-pulse irradiation. The physical mechanism of glass microwelding by double-pulse irradiation has been systematically investigated by measuring the dependence of the size of the heat-affected zone and the bonding strength on the delay time between the two pulses and analyzing the transient absorption induced by ultrafast laser pulses using a pump-probe technique . An increase in both the heat-affected zone and the bonding strength was found to be associated with an increase in the second-pulse absorption induced by the first pulse. The first pulse induces multiphoton or tunneling ionization, while the second pulse induces electron heating or avalanche ionization with a delay of up to 30 ps. Alternatively, the second pulse is absorbed by the localized state with a delay of as much as several nanoseconds. However, there remain issues to be clarified in order to optimize the process, such as the excitation and relaxation times of the excited electrons and how many photons are necessary for the second pulse absorption.
In this paper, the mechanism is systematically investigated by measuring the absorption of the second pulse for different laser powers as a function of the delay times after the first pulse irradiation. The second pulse absorption is different during the first 30 ps than it is during the next few nanoseconds. Therefore, the transient absorption change of the second pulse is decomposed into two time domains. The electronic excitation time from the valence to the conduction band, and the relaxation time of free electrons in the conduction band and of electrons trapped in the localized state are estimated by fitting the experimental results using rate equations.
2. Experimental setup for evaluation of the second-pulse absorption
The substrates are commercially available photosensitive glass (Foturan from Schott Glass) that consists of lithium aluminosilicate doped with trace amounts of silver, cerium, sodium, and antimony. An amplified femtosecond Er-fiber laser system (IMRA model FCPA μJewel D-400) generates 360-fs pulses at a wavelength of 1045 nm with a repetition rate of 200 kHz. The experimental setup is the same as that used for previous glass microwelding studies [16,17] except for the setup to measure the power of the transmitted laser pulses. The delay time between the two pulses is controlled by adjusting the optical path in the delay line using a high-precision stage, as confirmed by cross-correlation. The first pulse power is fixed at 155 mW, the power used for glass welding, while the second pulse power is varied from 5 to 155 mW. The p-polarized first and the s-polarized second pulses are focused into the glass substrate using an objective lens having a numerical aperture (NA) of 0.4. Figure 1 illustrates the scheme for measuring the energy of the second pulse transmitted by the photosensitive glass at different delay times. A polarized beam-splitter placed behind the glass substrate reflects the s-polarized second pulse to a power meter.
3. Estimate of the electronic excitation and relaxation times
It is considered that deposition of as much laser energy as possible into the glass results in efficient heating to produce a large molten zone for high-quality welding. Therefore, exploration of the electronic excitation and relaxation times is important for efficient transfer of the energy of the second pulse to the glass.
Using rate equations, based on previously proposed electronic processes in the photosensitive glass , the excitation and relaxation times are estimated by fitting the experimental data. The second pulse absorption differs in two delay time domains. Prior to 30 ps, the second pulse is absorbed by free electrons generated by the first pulse, resulting in electron heating or avalanche ionization, which imparts a high bonding strength during glass welding. Between 30 ps and a couple of ns, during which the bonding strength remains higher than that prepared by conventional single-pulse irradiation, the second pulse is absorbed by electrons trapped at a localized state. Figure 2 shows that a plot of optical density (OD) of the second pulse as a function of the delay time can be divided into these two time domains. The optical density is calculated from the measured transmittance of the second pulse OD –log10(IT/I0), where I0 and IT are the incident and transmitted laser energies, respectively. The incident powers of the first and second pulses are 155 mW at 200 kHz. An assumption is made that the reflection and scattering by the laser-induced plasma are negligible based on the results of Nahen et al. . Our previous experiments confirm that the reflection of the second pulse is nearly independent of the delay time. Therefore, the transmittance and absorbance add up to about 100%.
During time domain I, the two-level model of Fig. 3(a) is adopted, because free-electron generation and relaxation in the conduction band dominate. The electrons are excited from the valence to the conduction band by the first pulse. Although the interband excitation in photosensitive glass is elaborate as discussed later, a simple process, i.e., direct excitation from the valence band to the conduction band, is considered here to calculate the time for free electron generation. The resulting free electrons interact with the second pulse to weld the glass with a high bonding strength. The electrons eventually relax out of the conduction band. Therefore, it’s very important to explore the relaxation time of free electrons to determine the optimum timing of the second pulse. The rate equation of the two-level model is in general given by Eq. (1). Given that the full width at half maximum (FWHM) of the laser pulses is 360 fs, where . Here is the thermal excitation rate, is the relaxation rate, and and are the electron densities at time t in the valence and conduction band, respectively, where with and . Owing to the large energy gap of the photosensitive glass, can be ignored in the current case. In this time domain, free-electron absorption by the second pulse is dominant. Thus, the time-dependent variation of the OD of the second pulse is proportional to the free-electron density in the conduction band . According to the least-squares fitting in time domain , the excitation time and the relaxation time are therefore 0.98 and 20.4 ps, respectively. Accordingly, to achieve high-quality microwelding, the second pulse should arrive at a delay time between 1 and 20 ps. During this time interval, the number of electrons in the conduction band is maximal and most of the second laser pulse energy will be absorbed. In agreement with this conclusion, the highest bonding strength was achieved for delay times of 1–15 ps in our previous experiment. The excitation time is longer than the few hundred femtoseconds observed for typical glasses, because of the complexity of the interband excitation of electrons through various defect levels by multiphoton absorption . In addition, the relaxation time is much longer than 0.5 ps for fused silica , perhaps because the photosensitive glass has a more complex system than does fused silica.
Next, we simulate the relaxation times in the time domain II where the bonding strength is still higher than that for the conventional single-pulse irradiation sample. The absorption of the second pulse in this time domain arises from electrons trapped at a localized state such as a defect or exciton. Therefore, the three-level model of Fig. 3(b) is adopted in this domain. For simplicity, set because the electronic excitation takes place much earlier than the start of this time domain. The rate equations then becomeEq. (2), the electron density in the localized state is found to be
The variation of the OD in this time domain is proportional to because the absorption of the second pulse is due to electrons trapped at the localized state. Therefore, the relaxation time from the conduction band to the localized state and from the localized state to the valence band can be obtained by fitting Eq. (3) to Fig. 2, resulting in 104.2 and 714.3 ps, respectively. This 104.2 ps relaxation time from the conduction band to the localized state is much longer than the 20.4 ps from the conduction band to the valence band calculated above. However, the relaxation rate of free electrons out of the conduction band is expected to be constant. Thus, there may be another intermediate state that has a relaxation time of a few tens of picoseconds. The electrons could first relax from the conduction band to the intermediate state with a time of ~20 ps, and then further decay to the localized state with a relaxation time of ~80 ps. This idea would explain the small peak observed near 100 ps in Fig. 2.
The relaxation time from the localized state to the valence band is calculated to be 714.3 ps. One of the possible origins for the localized state may therefore be a self-trapped exciton, because the excitons have a typical lifetime of about 1 ns in silica glass at room temperature . Another possibility is the lattice defect.
4. Determination of the number of photons for the second pulse absorption
Multiphoton absorption inducing the interband excitation is dominant for conventional single-pulse irradiation. However, double-pulse irradiation can more efficiently deposit the laser energy in the glass, resulting in higher bonding strength. To demonstrate the effect, the number of photons absorbed during the second pulse irradiation is estimated in each time domain. For this estimation, the dependence of the transient absorption during the second pulse irradiation on the delay time for different second pulse powers was measured as shown in Fig. 4.
4.1 The number of photons absorbed in time domain I
The photosensitive glass has an elaborate electronic excitation process due to its complex composition. The electrons in the valence band are first excited to an intermediate state and then they are further excited to the conduction band to generate free electrons , resulting in the two-step excitation process depicted in Fig. 5. When the second pulse is incident at a delay time of between 1 and 20 ps (which are the excitation and relaxation times of free electrons calculated above), there are two possible absorption channels for the second pulse. One possibility is interband excitation via a defect level, and the other channel is absorption by free electrons. For the first step of the interband process [24, 27], an energy larger than 3.3 (3.9) eV is necessary, corresponding to 3 (4) photons of the femtosecond laser. For the second step, between 3.2 and 4.8 eV is needed, corresponding to between 3 and 5 photons. Meanwhile, free-electron absorption of a single photon occurs. Therefore, single-, three-, four- and five-photon absorption processes are possible for the second pulse in time domain I.
Based on these considerations, absorption of the second pulse is given by Figure 6(a) plots the dependence of the absorbed power density of the second pulse on the incident laser power at a delay time of 15 ps where the largest bonding strength occurs. The black curve is derived from Fig. 4, whereas the red line is computed by fitting the data to Eq. (4). For the fitting, dI/dx was calculated as (IT – I0)/DOF where I0, IT are the incident and the transmitted laser intensities and DOF (Depth of Focus) = λ/NA2, and I was set at the laser intensity around the center of focal volume (I = (I0 + IT)/2). The fit is excellent and the absorption coefficients for single-, three-, four-, and five-photon absorption are calculated to be 9.96 × 102 cm–1, 3.19 × 10−9 cm3 W–2, 2.88 × 10−16 cm5 W–3, and 1.29 × 10−22 cm7 W–4, respectively.
Using these absorption coefficients, Fig. 6(b) graphs the laser power density absorbed in each process as a function of the incident power of the second pulse. This result indicates that single- and three-photon absorption are much more likely than four- or five-photon absorption. Thus, one concludes that interband excitation takes place by three-photon absorption in both steps, whereas free-electron absorption only by single photons. In the current case, the first pulse energy is only used for free electron generation since the first pulse cannot interact with free electrons due to the significantly longer excitation time of 0.98 ps (see Sec. 3) than the pulse width of 360 fs. In the meanwhile, once the free electrons are generated by the first pulse, the second pulse is more probably absorbed by the free electrons than interband excitation through the intermediate state due to single photon absorption. In fact, about 55% of the second laser energy is absorbed by the free electrons even at the largest power of 155 mW used for glass welding. This result explains why the highest bonding strength is obtained at a delay time of around 15 ps.
4.2 The number of photons absorbed in time domain II
Between 30 ps and a couple of ns, absorption of the second pulse by electrons trapped at the localized state continues to result in higher bonding strength compared with that prepared by conventional single-pulse irradiation . In this time domain, the second pulse can be absorbed both by the interband excitation and by the electrons trapped at the localized state, as shown in Fig. 7. The interband excitation is induced by the three-photon absorption discussed in Sec. 4.1. To achieve a higher bonding strength, the localized state absorption needs to be more efficiently induced than the interband excitation. Therefore, the number of photons required for the localized state absorption should be smaller than 3. Based on this consideration, the data are fit to the following four combinations at a delay time of 100 ps corresponding to the small peak in Fig. 2,
The results are plotted in Fig. 8 as the red lines. The combination of 1- and 3-photon absorption in Fig. 8(b) gives the best fit to the experimental results from Fig. 4 graphed by the black line. These results indicate that localized state absorption occurs via a single photon, since the interband excitation is induced by three photons. Consequently, the localized state is more efficiently excited than are free electrons by three-photon absorption. This explains why a higher bonding strength is observed in time domain II than for conventional single-pulse irradiation.
The absorption coefficients calculated using Eq. (6) are 8.29 × 102 cm–1 for single-photon absorption and 3.37 × 10−9 cm3 W–2 for three-photon absorption. Figure 9 plots the laser power density absorbed by single and three photons for different second pulse powers using the calculated absorption coefficients at a delay time of 100 ps. Even at the largest power of 155 mW, as used for glass welding, about 46% of the energy of the second pulse is absorbed by the localized state to form the excited-localized state. There are three channels for relaxation of the excited-localized state, which are nonradiative transitions to its grand state and the valence band and a radiative transition to its grand states. The former two processes efficiently transform the absorbed laser energy into heat, while the latter one is nonthermal process. Since the radiative process usually occurs much later than the nonradiative processes, the nonradiative process is much more efficiently induced , resulting in more efficient heat generation which is responsible for a higher bonding strength than for single-pulse irradiation.
The physical mechanism of photosensitive glass microwelding by femtosecond double-pulse irradiation was experimentally and theoretically investigated by measuring the transient absorption of the second pulse induced by the first pulse. The second-pulse absorption arises from electronic excitation and relaxation processes that depend on the delay time in two different domains. In time domain I, ranging from 0 to 30 ps, the excitation and relaxation times of the free electrons were estimated to be 0.98 and 20.4 ps, respectively, whereas in time domain II (from 30 ps to several ns), the relaxation time from the conduction band to the localized state and from the localized state to the valence band were calculated to be 104.2 and 714.3 ps, respectively. Furthermore, we found that single-photon absorption of the second pulse by free electrons dominates in time domain I, which results in the highest possible bonding strength. Meanwhile in time domain II, the second pulse is absorbed by the localized state by a single photon, and approximately 46% of its energy is transferred to the localized state at the power of 155 mW that is used for glass welding. This localized state absorption results in a higher bonding strength than for conventional single-pulse irradiation. The single-photon absorption of the 1045-nm beam by the localized state occurs during time domain II relative to the arrival of the first pulse. These results suggest a new method of combining femtosecond irradiation with a nanosecond laser for efficient microwelding of glass.
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